I have decided to do Stronglifts 5x5. Can anyone provide me with advice on how to properly combine this with my MA training? I have kickboxing on monday, wednesday and friday evenings, bjj/grappling on tuesday and thursday and if possible (I deliver mail on saturdays) a seperate MMA class on saturday. I was thinking of using my free sunday for lifting weights at least but what would be the best way to do the other 2/3 days of the stronglifts programme? I don't like the idea of cutting back on MA training....

I wakeup at 6am most days and lift in the morning. You only really need 2 days a week of lifting, if you can get 3 that's good, but you can manage with 2 it just means your gains are a little slower.
Your lifting should be a supplement to your MA training, you should focus on it as much as you focus on any other SINGLE aspect of your training. So if you box 2-3 times a week, do BJJ 2-3 times a week, etc... then you should lift 2-3 times a week. Treat it like any other aspect of your training. Schedule it like it's a class.
If you are using the weights at your MMA gym then block aside an extra 45 minutes or so and show up before your grappling class and lift.

I wakeup at 6am most days and lift in the morning. You only really need 2 days a week of lifting, if you can get 3 that's good, but you can manage with 2 it just means your gains are a little slower.
Your lifting should be a supplement to your MA training, you should focus on it as much as you focus on any other SINGLE aspect of your training. So if you box 2-3 times a week, do BJJ 2-3 times a week, etc... then you should lift 2-3 times a week. Treat it like any other aspect of your training. Schedule it like it's a class.
If you are using the weights at your MMA gym then block aside an extra 45 minutes or so and show up before your grappling class and lift.

Getting up early is not really an option because the MA trainings are in the evening and I would not have enough time to sleep. I definitely want to train kickboxing 3 times a week, do grappling/BJJ 2 times a week AND lift 3 times a week. My only concern was whether this would cause overtraining or not. I'd be lifting weights at my MMA gym and I was thinking I'd lift on sundays (when there's no MA training) tuesday or wednesday before or after MA class and thursday or friday before or after MA training. I understand I'll have to eat a fucking lot but I'm totally OK with that.

Getting up early is not really an option because the MA trainings are in the evening and I would not have enough time to sleep. ...

“Sleep? Sleep is for those who are broke! I don’t sleep. I have an opportunity to make a dream become a reality.” 50 Cent

Seriouly one needs rest but i doubt you are near overtraining.
Most people who think they are overtraining or are worried about it, are not;
conversely those that are, seldom recognize it.
Often times what is attributed to overtraining could be addressed by something like better hydration/nutrition or a more comprehensive workout regimen as opposed to decreasing the athlete's workload.

I'm in my 40's and pretty much do what Kint describes, but i sub in a bit of recreational stuff fairly regularly, ie. surfing, hiking, paddling.
I work for myself but i often end up working til late and starting early for weeks at a time without a day off of work.
I still try to train daily, with one full "rest" day/week.
HTFU.

I work with quite a few high level lifters and triathletes (among others) and as disparate as those goals may be, the successful ones generally workout at least twice a day too.
Most of these people have day jobs, families etc.
The same goes for the successful recreational athletes, MAists etc. i know and work with.

I usually eat 3 or so boiled eggs before I lift in the AM, then have a protein berry smoothy made using coconut milk afterwards.

I lift 4 out of every 5 days and train BJJ 3-4 days a week usually for 2-3 hours a day. I also work full time. I sleep about 6 hours a night and as long as my diet is good (I eat Paleo about 90% of the time) i have plenty of energy.